Cfrgtkky

I have the code below to draw the terminal faces of a cylinder shown in horizontal direction.
I would like to complete the figure with the 2 lines that show the wall tube.

I guess there is something to do with:

tdplottransformmainscreen{?}{?}{?}

draw[tdplot_screen_coords] (??,??) -- (??,??);

Here is my code:

tdplotsetmaincoords{70}{120}

begin{tikzpicture}[scale=1.5, tdplot_main_coords]

%

% set some parameterts 

def ra{3.5};

def dfi{-25};

def dr{0.5};

def tetM{150};

def rM{2.5};

%

% draw axis

draw[line width=0.3mm,->,>={Latex[length=6]}](0,0,0)--(3,0,0)node[below]{emph{x}};

draw[line width=0.3mm,->,>={Latex[length=6]}](0,0,0)--(0,7,0)node[above]{emph{y}};

draw[line width=0.3mm,->,>={Latex[length=6]}](0,0,0)--(0,0,7)node[left=-3pt]{emph{z}};

draw[line width=0.7mm,-stealth](0,0)--(1,0)node[pos=0.9, above]{$vec{u}_x$};

draw[line width=0.7mm,-stealth](0,0)--(0,1)node[pos=0.8, below]{$vec{u}_y$};

draw[line width=0.7mm,-stealth](0,0,0)--(0,0,1)node[pos=0.7, left]{$vec{u}_z$};

%

% draw the back disk face

tdplotsetrotatedcoords{0}{90}{0}

coordinate (Shift) at (-9,0,0);

tdplotsetrotatedcoordsorigin{(Shift)}

begin{scope}[tdplot_rotated_coords]

draw ({ra},0) arc[start angle=0, delta angle=360, radius={ra}];

end{scope}

%

% draw the front disk face

tdplotsetrotatedcoords{0}{90}{0}

coordinate (Shift) at (0,0,0);

tdplotsetrotatedcoordsorigin{(Shift)}

begin{scope}[tdplot_rotated_coords]

draw [thick]({ra},0) arc[start angle=0, delta angle=360, radius={ra}];

coordinate (M) at (tetM:rM);

coordinate (Mp) at (tetM+dfi:rM);

coordinate (Mr) at (tetM:rM+dr);

coordinate (Mpr) at (tetM+dfi:rM+dr);

fill[gray!50,opacity=0.5](tetM:{rM}) arc[start angle=tetM, delta angle=dfi, radius={rM}] -- (Mpr) arc[start angle=tetM+dfi, delta angle=-dfi, radius={rM+dr}]--(M);

draw [line width=0.7mm](tetM:{rM}) arc[start angle=tetM, delta angle=dfi, radius={rM}] -- (Mpr)node[pos=0.5,below,sloped]{$dr$} arc[start angle=tetM+dfi, delta angle=-dfi, radius={rM+dr}]--(M);

draw[fill,red](tetM+dfi/2:rM+dr/2)circle(1.5pt);

draw[line width=0.7mm,->,>=Stealth,red]({tetM+dfi/2}:rM+dr/2)--++(0,0,1.5)node[below right=-3pt]{$dvec{S}$};

draw[line width=0.7mm](M)--(tetM:0)node[pos=0.3,above,sloped]{$r$};

draw[dashed](tetM:0)--(tetM:5);

draw[dashed](tetM+dfi:0)--(tetM+dfi:5);

draw [-{>[length=6]},thick](180:{4}) arc[start angle=180, delta angle=-180+tetM, radius={4}]node[pos=0.5,above]{$theta$};

draw [-{>[length=6]},line width=0.7mm](tetM:{4}) arc[start angle=tetM, delta angle=dfi, radius={4}]node[pos=0.5,above right=3pt]{$dtheta$};

end{scope}

Something like this?

documentclass[tikz,border=3.14mm]{standalone}

usepackage{tikz-3dplot}

usetikzlibrary{3d,arrows.meta,calc}

begin{document}

tdplotsetmaincoords{70}{120}

begin{tikzpicture}[scale=1.5, tdplot_main_coords]

  %

  % set some parameters 

  defra{3.5};

  defdfi{-25};

  defdr{0.5};

  deftetM{150};

  defrM{2.5};

  %

  % draw axis

  draw[line width=0.3mm,->,>={Latex[length=6]}](0,0,0)--(3,0,0)node[below]{emph{x}};

  draw[line width=0.3mm,->,>={Latex[length=6]}](0,0,0)--(0,7,0)node[above]{emph{y}};

  draw[line width=0.3mm,->,>={Latex[length=6]}](0,0,0)--(0,0,7)node[left=-3pt]{emph{z}};

  draw[line width=0.7mm,-stealth](0,0)--(1,0)node[pos=0.9, above]{$vec{u}_x$};

  draw[line width=0.7mm,-stealth](0,0)--(0,1)node[pos=0.8, below]{$vec{u}_y$};

  draw[line width=0.7mm,-stealth](0,0,0)--(0,0,1)node[pos=0.7, left]{$vec{u}_z$};

  %

  % draw the back disk face

  tdplotsetrotatedcoords{0}{90}{0}

  coordinate (Shift) at (-9,0,0);

  tdplotsetrotatedcoordsorigin{(Shift)}

  begin{scope}[tdplot_rotated_coords]

  draw ({ra},0)  arc[start angle=0, delta angle=360, radius={ra}];

  end{scope}

  %

  % draw the front disk face

  tdplotsetrotatedcoords{0}{90}{0}

  coordinate (Shift) at (0,0,0);

  tdplotsetrotatedcoordsorigin{(Shift)}

  path (-9,0,0) coordinate (M2);

  begin{scope}[canvas is yz plane at x=0]

    path (0,0) coordinate (M1);

    shade let p1=($(M1)-(M2)$),n1={atan2(y1,x1)} in 

     [top color=black,bottom color=black!80,middle color=gray!20,shading angle=n1,

      opacity=0.8]

     ($(M1)+(n1+90:ra)$) -- ($(M2)+(n1+90:ra)$)

     arc(n1+90:n1+270:ra) -- ($(M1)+(n1+270:ra)$)

     arc(n1+270:n1+90:ra);

  end{scope}

  begin{scope}[tdplot_rotated_coords]

    draw [thick]({ra},0) arc[start angle=0, delta angle=360, radius={ra}];

    coordinate (M) at (tetM:rM);

    coordinate (Mp) at (tetM+dfi:rM);

    coordinate (Mr) at (tetM:rM+dr);

    coordinate (Mpr) at (tetM+dfi:rM+dr);

    fill[gray!50,opacity=0.5](tetM:{rM}) arc[start angle=tetM, delta angle=dfi, radius={rM}] -- (Mpr) arc[start angle=tetM+dfi, delta angle=-dfi, radius={rM+dr}]--(M);

    draw [line width=0.7mm](tetM:{rM}) arc[start angle=tetM, delta angle=dfi, radius={rM}] -- (Mpr)node[pos=0.5,below,sloped]{$dr$} arc[start angle=tetM+dfi, delta angle=-dfi, radius={rM+dr}]--(M);

    draw[fill,red](tetM+dfi/2:rM+dr/2)circle(1.5pt);

    draw[line width=0.7mm,->,>=Stealth,red]({tetM+dfi/2}:rM+dr/2)--++(0,0,1.5)node[below right=-3pt]{$dvec{S}$};

    draw[line width=0.7mm](M)--(tetM:0)node[pos=0.3,above,sloped]{$r$};

    draw[dashed](tetM:0)--(tetM:5);

    draw[dashed](tetM+dfi:0)--(tetM+dfi:5);

    draw [-{>[length=6]},thick](180:{4}) arc[start angle=180, delta angle=-180+tetM, radius={4}]node[pos=0.5,above]{$theta$};

    draw [-{>[length=6]},line width=0.7mm](tetM:{4}) arc[start angle=tetM, delta angle=dfi, radius={4}]node[pos=0.5,above right=3pt]{$dtheta$};

  end{scope}

end{tikzpicture}

end{document}

Notice that I used the 3d library for that because I find it more intuitive. And I think you could use it all over instead of switching to all these rotated coordinate systems. Here is what I got.

documentclass[tikz,border=3.14mm]{standalone}

usepackage{tikz-3dplot}

usetikzlibrary{3d,arrows.meta,calc}

begin{document}

tdplotsetmaincoords{70}{120}

begin{tikzpicture}[scale=1.5, tdplot_main_coords]

  %

  % set some parameters 

  defra{3.5};

  defdfi{-25};

  defdr{0.5};

  deftetM{150};

  defrM{2.5};

  %

  % draw the back disk face

  begin{scope}[canvas is yz plane at x=-9]

   draw (0,0) coordinate (M2) circle[radius=ra];

  end{scope}

  %

  % draw the front disk face

  %path (-9,0,0) coordinate (M2);

  begin{scope}[canvas is zy plane at x=0,xscale=-1]

    path (0,0) coordinate (M1);

    shade let p1=($(M1)-(M2)$),n1={atan2(y1,x1)} in 

     [top color=black,bottom color=black!80,middle color=gray!20,

     shading angle=n1+90,opacity=1]

     ($(M1)+(n1-90:ra)$) -- ($(M2)+(n1-90:ra)$)

     arc(n1-90:n1+90:ra) -- ($(M1)+(n1+90:ra)$)

     arc(n1+90:n1-90:ra);

    shade let p1=($(M1)-(M2)$),n1={atan2(y1,x1)} in 

     [top color=black,bottom color=black!80,middle color=gray!20,

     shading angle=n1+90,opacity=0.6]

     ($(M1)+(n1+90:ra)$) -- ($(M2)+(n1+90:ra)$)

     arc(n1+90:n1+270:ra) -- ($(M1)+(n1+270:ra)$)

     arc(n1+270:n1+90:ra);

    draw[thick] (M1) circle [radius=ra];

    coordinate (M) at (tetM:rM);

    coordinate (Mp) at (tetM+dfi:rM);

    coordinate (Mr) at (tetM:rM+dr);

    coordinate (Mpr) at (tetM+dfi:rM+dr);

    fill[gray!50,opacity=0.5](tetM:{rM}) arc[start angle=tetM, delta angle=dfi, radius={rM}] -- (Mpr) arc[start angle=tetM+dfi, delta angle=-dfi, radius={rM+dr}]--(M);

    draw [line width=0.7mm](tetM:{rM}) arc[start angle=tetM, delta angle=dfi, radius={rM}] -- 

    (Mpr)node[pos=0.5,below,sloped,rotate=90]{$mathrm{d}r$} arc[start angle=tetM+dfi, delta angle=-dfi, radius={rM+dr}]--(M);

    draw[fill,red](tetM+dfi/2:rM+dr/2) coordinate (P) circle(1.5pt);

    draw[line width=0.7mm](M1)--(M)node[pos=0.7,above,sloped,rotate=90]{$r$};

    draw[dashed](tetM:0)--(tetM:5);

    draw[dashed](tetM+dfi:0)--(tetM+dfi:5);

    draw [-{>[length=6]},thick](180:{4}) arc[start angle=180, delta angle=-180+tetM, radius={4}]node[pos=0.5,above]{$theta$};

    draw [-{>[length=6]},line width=0.7mm](tetM:{4}) arc[start angle=tetM, delta angle=dfi, radius={4}]node[pos=0.5,above right=3pt]{$dtheta$};

  end{scope}

  draw[line width=0.7mm,->,>=Stealth,red](P)--++(1.5,0,0)node[below right=-3pt]

  {$mathrm{d}vec{S}$};

  % draw axes

  draw[line width=0.3mm,->,>={Latex[length=6]}](0,0,0)--(3,0,0)node[below]{emph{x}};

  draw[line width=0.3mm,->,>={Latex[length=6]}](0,0,0)--(0,7,0)node[above]{emph{y}};

  draw[line width=0.3mm,->,>={Latex[length=6]}](0,0,0)--(0,0,7)node[left=-3pt]{emph{z}};

  draw[line width=0.7mm,-stealth](0,0)--(1,0)node[pos=0.9, above]{$vec{u}_x$};

  draw[line width=0.7mm,-stealth](0,0)--(0,1)node[pos=0.8, below]{$vec{u}_y$};

  draw[line width=0.7mm,-stealth](0,0,0)--(0,0,1)node[pos=0.7, left]{$vec{u}_z$};  

end{tikzpicture}

end{document}